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<a href="CAD_using_en.htm">See operating CAD</a>


<h1>Vectors</h1>


Vectors define a direction and do not have a position.

Vectors use the identification letter D ("Direction").

There are the following standard vectors:
  DX DY DZ
  corresponding to the absolute directions

  DIX DIY DIZ
  corresponding to the reverse absolute directions


Display of Vectors:
- Vectors are only temporarly represented;
- standard-vectors are displayed in the lower right corner
- scan through defined vectors with the PageUp or PageDown button
- Standardized vectors (with length 1) as dashed line, otherwise as full line.


Define a vector:
- select a line or 2 points or a polygon
- select a circle or plane (normal-vector)
- select one of the standard-vectors from the vectors displayed in
    the lower right corner. 
- select a defined vector with the PageUp or PageDown button
- key in vector:
  standard-vector DX or DY or DZ or DIX or DIY or DIZ
  or defined-vector eg "D12"
  or the x/y/z-coordinates; eg "D(0 0 1)" defines a Z-vector
  or one or two angles; eg "D(ANG(45))" or "D(ANG(45) ANG(45))"


<u>Example:</u>
# Vector 1 = direction negative X-Achse
D1=DIX
# Vektor 2 = into direction x=1, y=1 in the XY-plane
D2=D(1 1 0)



<p><a name="Copy"></a></p>
  <h2>Vectors from Copy function</h2>
Objectselections create this formats:

# Vector from Line:
D(L{nr})
<u>Example:</u>
L20=P(0 0 0) P(100 10 0)
D20=D(L20)


# Vector from Polygon segment
# or Vector from Line in CCV:
D({obj} MOD({SegmentNummer}))


# Vector on circle, B-Spline, clothoid, ellipse:
 D#={C#|S#}) {lpar})
<u>Example:</u>
# Vector on circle:
C20=P(0 0 0) 12
D20=D(C20 0.5)


# Vector from Line in CCV
# or Vector from Polygonsegment in CCV:
P({obj} MOD({CCV-SegmentNummer}) MOD({SegmentNummer}))


<u>Example:</u>
# Vector from 1.Segment of CCV S26 (a Line):
P(S26 MOD(1))



<hr>
<a name="F0"></a>
<h2>VEC cartesian</h2>
Create vector.

   BaseVector       basevector
   [Angle-Rot.]     rotation around the z-axis of the active construction-plane
   [Angle-Tilt]     <a href="CAD_Base_en.htm#ANGT">tilting angle</a> in the active construction-plane
   [Length]         Definition of vector length
   [REVers]         Reverse Direction ("REV"; also with Page-Down key)


  <B>Definition basevector:</B>
    Definition by entering the components of the axis (eg "0 0 1", a z-vector)

    Or input of a standard vector (eg "DX")
      Standardvectors are DX DY DZ DIX DIY DIZ.

    Or a defined vector (eg "D20"; with Page-Up or Down key or select
      from the objectbrowser (left side))

    Or selection of a line or polygonsegment (or polygonsegment in CCV)
      or plane or plain surface.


Examples:
# Vector from X,Y,Z-components:
D3=D(0.7 0 0.7)

# X-Vector rotated 30 deg. around the z-axis of the active construction-plane
#   an then 60 deg. tilted.
D4=DX ANG(30) ANG(60)

# Vector reverted
D5=D4 REV




<a name="F1"></a>
<h2>VEC objects</h2>
Vectors parallel or right-angled to existing objects.

   Obj1              Line or curve or surface
   [Point (on obj)]  basepoint for vector
   [PT or VC]        additional object (e.g. for normal vector)
   [Length]          Definition of vector length
   [REVers]          Reverse Direction ("REV"; with Page Down key)
   [parallel-across] parallel (tangential) or normal (rectangular)



<b>Parallel Vector:</b>

  Vector tangential to curve through point on this curve:
   Obj1              Line or curve or surface
   [Point (on obj)]  point on this curve / surface

  Vector parallel to Vector or Line, cornerpoint
    Obj1              direction - Vector or Line
    [Point (on obj)]  Startpoint
    [PT or VC]        point (cornerpoint)
    PARL oder CX      PARL: Vector along Obj1 from Startpoint to cornerpoint
                      CX:   Vector normal to direction
                      default: normal to plane from Obj1 - cornerpoint

  Vector parallel to 2 points, cornerpoint
    Obj1              Startpoint
    [Point (on obj)]  point on Vector / Line
    [PT or VC]        point (cornerpoint)
    PARL oder CX      PARL: Vector along Startpoint - Point-on-OBj to cornerpoint
                      CX:   Vector normal to Startpoint - Point-on-OBj
                      default: normal to plane from 3 points

  Vector in surface parallel to Isoparametric direction U or
                      Isoparametric direction V
    Obj1              surface oder plane
    [Point (on obj)]  point on surface
    PARL oder CX      PARL: vector at Point-on-OBj into direction U
                      CX:   vector at Point-on-OBj into direction V
                      default: vector at Point-on-OBjnormal to surface


<b>Normal Vector:</b>
  Normal vector for circle or plane or ellipse
    Obj.1                 select  circle, plane or ellipse
  
  Normal vector to 2 line Segments (crossproduct):
    3 points
    line, point
    2 lines
    The result (the normal vector) is the cross product of 2 input vectors.

  Normal vector surface (until now only B-SplineSurface)
    Obj.1                 select surface and -
    [Point (on Obj)]      a point on this surface



Examples:

# Normal vector to circle
D20=C20

# Tangential vector to circle
D21=C20 P(C20 0.2)

# Vector between points P1, P2; length 100.
D5=P1 P2 VAL(100)

# Normal vector to line L20:
D20=L20 DZ

# X-axis-Vector of plane R20
D20=R20 PARL




<hr>
The following commands must be produced manually:

<h2>Vector-Multiplication / Divison</h2>
D21 = D20 * 2
D22 = D20 / 2






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